Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic FlowThe author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models. Haberman develops the method of characteristics to analyze the nonlinear partial differential equations that describe traffic flow. Fan-shaped characteristics describe the traffic situation that occurs when a traffic light turns green and shock waves describe the effects of a red light or traffic accident. Although it was written over 20 years ago, this book is still relevant. It is intended as an introduction to applied mathematics, but can be used for undergraduate courses in mathematical modeling or nonlinear dynamical systems or to supplement courses in ordinary or partial differential equations. |
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Page 28
... limit . Hold to high limit ; use judg- ment as to low limit . Plug thread limit gauge for diameter of magazine filling hole . Hold the minimum limit ; judgment as to high limit . use Width of slots . Use judgment . Depth of recess in ...
... limit . Hold to high limit ; use judg- ment as to low limit . Plug thread limit gauge for diameter of magazine filling hole . Hold the minimum limit ; judgment as to high limit . use Width of slots . Use judgment . Depth of recess in ...
Page 25
... LIMIT OVERRIDE ELECTION TURNOUT AND SELECTED DISTRICT CHARACTERISTICS : CALIFORNIA UNIFIED SCHOOL DISTRICTS , 1973-74 THROUGH 1977-78 Election Characteristics Increase in Revenue Limit Required Tax Rate Increase Revenue Limit Proposed ...
... LIMIT OVERRIDE ELECTION TURNOUT AND SELECTED DISTRICT CHARACTERISTICS : CALIFORNIA UNIFIED SCHOOL DISTRICTS , 1973-74 THROUGH 1977-78 Election Characteristics Increase in Revenue Limit Required Tax Rate Increase Revenue Limit Proposed ...
Page 29
... limit stands . After three cuts , the ratio was improved to 2.1 in the selection treatment , but had deteriorated to 0.5 in the diameter - limit stands . Questions have been raised about the influence of the diameter limits on the PEF ...
... limit stands . After three cuts , the ratio was improved to 2.1 in the selection treatment , but had deteriorated to 0.5 in the diameter - limit stands . Questions have been raised about the influence of the diameter limits on the PEF ...
Page 23
... limits that we encounter in the field of international human rights. Its topics underscore their variety—what they limit, how they limit, why they limit—within that ample field. The goal is not to build a unifying structure of powers and ...
... limits that we encounter in the field of international human rights. Its topics underscore their variety—what they limit, how they limit, why they limit—within that ample field. The goal is not to build a unifying structure of powers and ...
Page 27
... limit as defined by 970 CMR 4.03 and complies with the requirements of 970 CMR 4.05 . A qualifying contribution shall not include a contribution : ( a ) made in the form of a loan , ( b ) refunded or intended to be refunded to a ...
... limit as defined by 970 CMR 4.03 and complies with the requirements of 970 CMR 4.05 . A qualifying contribution shall not include a contribution : ( a ) made in the form of a loan , ( b ) refunded or intended to be refunded to a ...
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude analysis applied approximately Assume birth calculated called cars characteristics Consider constant continuous corresponding curve decreases delay depends derived described determine differential equation discussed distance energy equal equilibrium population equilibrium position equivalent example exercise experiments expression Figure first fish flow force formulate friction function given growth rate hence highway illustrated increases initial initial conditions integral isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane possible probability problem region result roots sharks shock Show shown in Fig simple sketched sketched in Fig solution solve species spring spring-mass system stable straight line Suppose tion traffic density traflic trajectories unstable variables velocity yields zero